Magneto-oscillations in the current through single-barrier heterostructures have been observed, due to electrons tunneling from a 2DEG in a lightly-doped emitter into interfacial Landau states (skipping orbits) in the collector contact. We have calculated the dependence of tunnel current on magnetic field and bias voltage using the Bardeen transfer Hamiltonian approach within a WKB approximation. A physical interpretation of the results is given in terms of the effect of the magnetic field on barrier transmission and on the amplitudes of the confined wave functions. The model is extended to double-barrier structures. © 1990.